An asymmetric double-slit interferometer for small and large quantum particles

TL;DR

This paper investigates how the finite size of particles affects interference patterns in an asymmetric double-slit setup, extending quantum interference theory to larger particles like molecules.

Contribution

It provides a detailed analytical description of interference considering particle size, including cases where particle diameter is comparable to slit width.

Findings

Transverse momentum distribution remains unaffected by distance from slits.

Space distribution of particles depends strongly on the distance from the slits.

Finite particle size significantly influences interference patterns in asymmetric double-slit experiments.

Abstract

Quantum theory of interference phenomena does not take the diameter of the particle into account, since particles were much smaller than the width of the slits in early observations. In recent experiments with large molecules, the diameter of the particle has approached the width of the slits. Therefore, analytical description of these cases should include a finite particle size. The generic quantum interference setup is an asymmetric double slit interferometer. We evaluate the wave function of the particle transverse motion using two forms of the solution of Schrodinger's equation in an asymmetric interferometer: the Fresnel-Kirchhoff form and the form derived from the transverse wave function in the momentum representation. The transverse momentum distribution is independent of the distance from the slits, while the space distribution strongly depends on this distance. Based on the transverse momentum distribution we determined the space distribution of particles behind the slits. We will present two cases: a) when the diameter of the particle may be neglected with respect to the width of both slits, and b) when the diameter of the particle is larger than the width of the smaller slit.